Question

In the following geometric sequence, find (i) the 7th term; (ii) the nth term:-1/3, 3/4, -9/8, .....

Answer 1

Given the geometric sequence:

`-(1)/(2),(3)/(4),(-9)/(8),\ldots.`

The common ratio will be:

`r=(3)/(4)/-(1)/(2)=(3)/(4)\cdot-2=-(3)/(2)`

The general rule of the geometric sequence will be:

`a_n=a_1\cdot r^(n-1)`

so, a7 will be:

`a_7=-(1)/(2)\cdot(-(3)/(2))^(7-1)=-(1)/(2)\cdot(-(3)/(2))^6=-(729)/(128)`

And an will be:

`a_n=(-(1)/(2))\cdot(-(3)/(2))^(n-1)_{}`